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21 (a) A graph is drawn below: y | | | | | | +----------------- x Explain how you know that y is not directly proportional to x - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

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21-(a)-A-graph-is-drawn-below:-----y----|----|-----|-------|---------|-----------|-----------+------------------x-----Explain-how-you-know-that-y-is-not-directly-proportional-to-x-OCR-GCSE Maths-Question 21-2017-Paper 1.png

21 (a) A graph is drawn below: y | | | | | | +----------------- x Explain how you know that y is not directly pro... show full transcript

Worked Solution & Example Answer:21 (a) A graph is drawn below: y | | | | | | +----------------- x Explain how you know that y is not directly proportional to x - OCR - GCSE Maths - Question 21 - 2017 - Paper 1

Step 1

Explain how you know that y is not directly proportional to x.

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Answer

To determine that y is not directly proportional to x, we can observe the graph provided. If y were directly proportional to x, the line would pass through the origin (0, 0). In this case, the graph does not pass through this point, indicating that y varies with x but not in a directly proportional manner.

Step 2

Work out q when r is 25.

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Answer

Since q is directly proportional to r, we can express this relationship as:

q=kimesrq = k imes r

where k is the constant of proportionality.

To find k, we can use the values given: 68 when r is 20:

68=kimes2068 = k imes 20

Solving for k gives:

k=6820=3.4k = \frac{68}{20} = 3.4

Now, substituting r = 25 into the equation:

q=3.4×25=85q = 3.4 \times 25 = 85

Thus, when r is 25, q is 85.

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